US economy looks better, so why do we worry?

The U.S. economy has churned out some pretty encouraging news lately, but plenty of skeptical Americans still have much anxiety about this recovery.

Major questions remain about certain aspects of the health of the economy, including stagnant wage growth, unemployment and corporate taxes.

(Watch President Barack Obama discuss the state of the American economy in an exclusive interview with CNBC's Steve Liesman, Thursday at 5 p.m. ET on CNBC-TV and CNBC.com)

After some weak numbers at the beginning of the year, the U.S. economy may be nearing a crucial turning point, economists told CNBC.

"The economy is mediocre," said Joel Naroff, president of Naroff Economic Advisors. "But it's getting better by the month."

Michael Nagle | Bloomberg | Getty Images

A job seeker leaves his contact information at a career fair held by Union Square Hospitality Group in New York.

A Gallup poll from July found that Americans are less worried about unemployment and jobs issues in the U.S. than in previous months, although 14 percent still said they think it is the most important problem facing the country.

Despite these concerns, Michael Feroli, J.P. Morgan's chief U.S. economist, said he sees a promising employment picture. Jobs growth "seems to be doing as well as one could hope," he said.

Some worry, however, that strong jobs numbers—U.S. companies gained 288,000 nonfarm payrolls as the unemployment rate dropped to 6.1 percent in June—are masking less rosy economic trends. Not only are marginally attached workers still a significant part of the "regular" employment figure, but many Americans have become discouraged and disappeared from the workforce altogether.

"I am concerned about the labor market," Wells Fargo senior economist Mark Vitner said in an email to CNBC. "We have so many people working part-time today that would like to find more meaningful work."

But as employment figures continue positive trends, wages have remained stagnant, and this is "the missing link in this whole economic recovery," Naroff said.

While jobs growth is usually expected to lag behind economic growth, workers' wages will trail positive employment trends, Naroff said. But as the economy begins to reach full employment (a point he estimates to be about nine months in the future), employers will be forced to increase pay to attract the best workers.

Wages should begin to rise in the next six months, Naroff projected. Feroli agreed, saying "we may be close to a turning point."

If this turning point comes, the Obama administration may see some alleviation of one of its major economic concerns: income inequality causing weak economic growth. As companies are forced to increase compensation, Naroff said, middle- and lower-class workers should begin to drive consumption growth.

Consumption remains a major worry for corporate America. In an earnings call Tuesday, McDonald's president Don Thompson said he has seen a bifurcation in spending habits wherein those making less than $45,000 annually are "a little bit tighter" with their discretionary spending than their higher-earning peers.

"Inequality is more than a buzzword," Vitner said, adding that income disparity is in part a function of job training, and so may be long-lasting regardless of any change in minimum wage.

The Obama administration's other major economic talking point has been the issue of American corporations conducting tax inversions—when firms shift their tax domicile overseas to avoid the burden of U.S. taxes. Several 2014 deals occurred for this purpose, including Chiquita Brands International's purchase of Ireland's Fyffes, but the significance for the overall economy is not clear.

While Feroli said he did not see inversions as a significant macroeconomic issue, Naroff said the practice could result in small businesses facing an increased tax burden.

"There's no such thing as a free tax break," Naroff said, explaining that these large corporations have exploited a loophole in the tax code to the same effect as a legislature-granted break. "If someone doesn't pay what their fair share of taxes should be, someone else will have to."

Read MoreSenate panel to debate wave of corporate tax-avoidance deals

Although Naroff said the country's tax policy remains one of the single largest problems plaguing its economy, Vitner said the U.S. continues to benefit from those hoping to enter its borders.

"The biggest bright spot is that for all our problems, the best, brightest and most ambitious entrepreneurs and workers still seek to come to America," he said. "As long as the Elon Musks of the world come to the USA so that they can change the world, we will be OK."